量子力學第七章習題-文庫吧資料
2025-05-18 22:26本頁面
【正文】 r,r( ??? ? 三重態(tài)： ????????)3(214)2(213)1(212),(),(),(SASASArrrrrr?????????。 )]()()()([)]()()()([2122/112/122/112/122/112/122/112/1)3()3(zzzzzzzzSSSSSSSSSS????????????????????? )]S()S([)]S()S([21 z12/1z22/1z22/1z12/1 ???? ???? )]S()S([)]S()S([21 z12/1z12/1z12/1z22/1 ???? ???? )]S()S([)]S()S([21 z12/1z22/1z12/1z22/1 ???? ???? 1210021 ?????)]()([)]()([21 22/112/122/112/1 zzzz SSSS ???? ????7 .8 設兩電子在彈性輳力場中運動，每個電子的勢能是2221)( rrU ???。設兩個 單粒子態(tài)為i?，j?，則體系可能的狀態(tài)為 )()()( 3211 qqq iii ????? )()()( 3212 qqq jjj ?????)]()()()()()()()()([311322313213qqqqqqqqqjiijiijii????????????? )]()()()()()()()()([311322313214qqqqqqqqqijjijjijj????????????? 證明 )3()2()1( , SSS ??? 和 A? 組成的正交歸一系。玻色子只有兩個可能的單粒子態(tài)。 設對應于2??nS的本征函數(shù)的矩陣表示為?????????baSn )(21?，則 ????????????????????????????babaii2c osc osc osc osc osc os2????????bbia ???? ??? c o s)c o s( c o s ???c os1c osc os??? ib由歸一化條件，得 22** ),(12121 bababa ???????????? ? ?? 1c os1c osc os 222 ???? aia??? 1c os1 2 2 ?? a?取 2c o s1 ???a ， 得 )c os1(2c osc os?????? ib ????????????????)c o s1(2c o sc o s1c o s1)(21?????iSn????????????????)c o s1(2c o sc o s1c o s1)(21?????iS n2121)c o s1(2c o sc o s2c o s110)c o s1(2c o sc o s012c o s1)(21????
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